This invention relates to method and apparatus for estimating transfer functions among multiple physiologic or biologic signals in the presence of feedback.
A living organism includes multiple physiological organ subsystems. While each of these subsystems performs a specific function, such as respiration or blood circulation, there is a complex interaction between them which adjusts their functioning. These adjustments adapt the organism to a variety of environmental conditions and tasks.
As an example, consider what occurs in the simple act of standing. A supine subject undergoes a variety of physiological adjustments when the subject stands up. Changing the direction of gravity results in a change in heart rate, blood pressure, and vascular tone. The physiological subsystems must come to a new equilibrium state that allows the subject to function under this new environmental condition. If, for example, vascular tone did not change upon standing, the blood would pool in the lower extremities. This pooling ultimately would result in a loss in consciousness as the brain is deprived of blood flow.
An understanding of the regulation of the physiology of the organism requires not only an understanding of each organ subsystem but also of their interactions. One difficulty is that each organ system is itself complex and any, in turn, consist of a large number of components. This complexity frequently makes a complete understanding of an organ subsystem impossible. However, the lack of understanding of the internal or fine-structure of an organ subsystem does not preclude an understanding of how that subsystem interacts with other organ subsystems.
The reason that the interactions may be studied without a detailed knowledge of the individual organ subsystems is that a complex system may be treated as a single unit or black-box about which nothing is known except for its stimulus (input) and response (output). By understanding the way a subsystem responds to a specific input, a mathematical description of that subsystem treated as a black-box may be developed. It so happens that, if the subsystem can be considered to have certain mathematical properties, the description developed for that one specific input is valid for all inputs.
This approach is reasonable in the study of physiological systems since it is actually only the stimuli and responses which are measured. For example, it is the heart rate (response) that is measured as a function of changes in arterial blood pressure (stimulus), and it is irrelevant that the functioning of the individual cell types of the heart cannot be determined. This systems approach to physiology has resulted in a greater understanding of the interactions between organ subsystems.
In order to characterize a black-box from input-output data, one must elicit the entire range of possible responses from the subsystem; such suitable inputs are called "informative". With real systems, it is often the case that the spontaneous fluctuations within the system are not informative. It is therefore necessary to enrich the inputs by adding exogenous broad-band noise in the form of external stimuli.
Many earlier efforts have been directed towards modeling the cardiovascular control system and estimating the transfer relations in the models. Robert Kenet, in his PhD thesis (Yale University, 1983), considered two transfer functions, heart rate to blood pressure and blood pressure to heart rate, operating in closed loop.
Kenet used parametric identification techniques but did not whiten the spontaneous heart rate fluctuations by introducing an external noise source. Instead, he analyzed data from dogs undergoing atrial fibrillation, which, although it does generate broadband ventricular heart rate, it essentially destroyed the baroreceptive feedback loop. Thus, Kenet was unable to accommodate both closed-loop physiologic function with broad-band signals.
Another group used multivariate autoregressive modeling to analyze heart rate and blood pressure signals without explicitly measuring respiration and without enriching the spontaneous fluctuations. However, their method was less general than Kenet's because it did not allow poles in either of the transfer functions. (See Analysis of Blood Pressure and Heart Rate Variability Using Multivariate Autoregressive Modeling, Kalli, S, Suoranta, R, Jokipii, M, and Turjanmaa, V. Computers in Cardiology Proceedings, IEEE Computer Society (1986); Applying a Multivariate Autoregressive Model to Describe Interactions Between Blood Pressure and Heart Rate, Kalli, S, Suoranta, R and Jokipii, M., Proceedings of the Third International Conference on Measurement in Clinical Medicine, pp 77-82, Edinburgh; (1986)).
Baselli et al. used parametric techniques to identify a closed-loop model of cardiovascular control that incorporated heart rate, blood pressure and respiration signals, but, they too did not whiten the spontaneous fluctuations in heart rate, and therefore, their methodology does not allow reliable identification of the causal transfer functions under the usual conditions of narrow band spontaneous fluctuations. (See Cardiovascular Variability Signals: Towards the Identification of a Closed-Loop Model of the Neural Control Mechanisms, Baselli, G, Ceruttie, S, Civardi, S, Malliani, S and Pagani, S.) IEEE Transactions on Biomedical Engineering, 35, p. 1033-1046 (1988)).
Non-parametric (frequency domain) methods have also been applied to cardiovascular system identification. These methods do not permit the separate estimation of the feedforward (G) and feedback (H) components of a system. Instead, one can estimate only the overall closed loop transfer function of the form G/(1+GH). In general there are many (G,H) pairs that are consistent with a given closed loop transfer function. (See Transfer Function Analysis of Autonomic Regulation 1. Canine Atrial Rate Response, Berger, R. D., Saul, J. P. and Cohen, R. J. American Journal of Physiology, vol. 256, Heart and Circulatory Physiology, vol. 25, pp H142-152, 1989) Berger et al. electrically stimulated either the vagus or sympathetic heart rate control systems in dogs at intervals generated by passing broad-band frequency modulated noise through an integrate-and-fire filter. This experiment achieved broad-band, open loop stimulation of the cardiovascular system. Kitney et al. performed similar experiments on rabbits, using a pulse-frequency modulated pseudo-random binary sequence to stimulate the cardiac depressor nerve (baroreceptor afferent). (See System Identification of the Blood Pressure Control System by Low Frequency Neural Stimulation, Kitney, R. I. and Gerveshi, C. M. Transactions of the Institute of Measurement and Control, vol. 4, pp 203-212, (1982)).
A noninvasive method for broadening the frequency content of heart rate and blood pressure fluctuations by whitening the respiratory perturbations was described by Berger et al. in U.S. Pat. No. 4,777,960 and applied experimentally in Transfer Function Analysis of Autonomic Regulation II. Respiratory Sinus Arrhythmia, J. P. Saul, R. D. Berger, M. H. Chen, R. J. Cohen, American Journal of Physiology, Volume 256, (Heart Circ. Physiology 25), p. H153-H161, 1988. However, because this work did not address the causal relationship between signals it does not provide a methodology for separately identifying the feed-forward and feedback transfer functions in a closed-loop system.
Parametric system identification techniques have been applied to control anti-hypertensive drug delivery in response to changes in blood pressure. (Parameter Identification and Adaptive Control for Blood Pressure, Walker, B. K, Chia, T.-L., Stern, K. S. and Katona, P. G. IFAC Symposium on Identification and System Parameter Estimation, pp 1413-1418, (1982); Adaptive Pole Assignment Control of Blood Pressures Using Bilinear Models, McInnis, B. C., Deng, L-z and Vogt, R., IFAC Symposium on Identification and System Parameter Estimation, pp 1209-1212, (1985)). Approaches in this field have one common element: the input is the drug infusion and the output is blood pressure. The goal is to determine a feedback control law that adequately regulates arterial blood pressure, which involves first identifying the open-loop feedforward path (i.e.: how blood pressure responds to a unit drug infusion).
Finally, several groups have constructed mathematical models of circulatory regulation and of circulatory mechanics. These models are designed to reproduce phenomena observed in many data sets or in particular exemplary ones, but are not designed to be fit to any individual's data. In fact, it would be impossible to find a unique best fit of these models' parameters to any particular data record; that is, they are not identifiable. Although the mathematical descriptions these models offer may use linear system elements, they do not serve the same purpose as the present invention. (See Identification of Respiratory and Cardiovascular Systems, D. A. Linkens IFAC Sumposium on Identification and System Parameter Estimation, pp 55-67, (1985)).
The present invention teaches how noise injected into one or more inputs can be used in conjunction with parametric system identification techniques to identify the n(n-1) possible transfer relationships (transfer functions in the frequency domain or impulse or other driving signal responses in the time domain), that relate n signals by all possible feedback and feedforward paths. This for the first time allows one to identify accurately, physiological transfer functions in the presence of feedback. For the purposes of this discussion, the term transfer function will be used to mean transfer relationships both in the frequency and in the time domains.